International Journal of Modern Physics C

This paper describes a correspondence between computational quantities commonly used to report computer performance measurements and mechanical quantities from classical Newtonian mechanics. It defines a set of three fundamental computational quantities that are sufficient to establish a system of computational measurement. From these quantities, it defines derived computational quantities that have analogous physical counterparts. These computational quantities obey three laws of motion in computational space. The solutions to the equations of motion, with appropriate boundary conditions, determine the computational mass of the computer. Computational forces, with magnitudes specific to each instruction and to each computer, overcome the inertia represented by this mass. The paper suggests normalizing the computational mass scale by picking the mass of a register on the CRAY-1 as the standard unit of mass.

The temperature behavior of a system of dipoles with long-range interactions has been simulated via a two-dimensional lattice Monte Carlo on a massively SIMD platform (Quadrics/APE100). Thermodynamic quantities have been evaluated in order to locate and to characterize the phase transition in absence of applied field. Emphasis is given to the code implementation on the SIMD architecture and to the relevant features which have been used to improve code capabilities and performances.

The probability of simultaneous occurrence of at least k spanning clusters has been studied by Monte Carlo simulations on the 2D square lattice with free boundaries at the bond percolation threshold p_c =1/2. It is found that the probability of k and more Incipient Spanning Clusters (ISC) have the values P(k>1) ≈ 0.00658(3) and P(k>2) ≈ 0.00000148(21) provided that the limit of these probabilities for infinite lattices exists. The probability P(k>3) of more than three ISC could be estimated to be of the order of 10^-11 and is beyond the possibility to compute such a value by nowadays computers. So, it is impossible to check in simulations the Aizenman law for the probabilities when k≫1. We have detected a single sample with four ISC in a total number of about 10¹⁰ samples investigated. The probability of this single event is 1/10 for that number of samples. The influence of boundary conditions is discussed in the last section.

We describe a simple framework for microsimulation of city traffic. A medium-sized excerpt of Dallas was used to examine different levels of simulation fidelity of a cellular automaton method for the traffic flow simulation and a simple intersection model. We point out problems arising with the granular structure of the underlying rules of motion.

This paper presents a day-to-day re-routing relaxation approach for traffic simulations. Starting from an initial planset for the routes, the route- based microsimulation is executed. The result of the microsimulation is fed into a re-router, which re-routes a certain percentage of all trips. This approach makes the traffic patterns in the microsimulation much more reasonable. Further, it is shown that the method described in this paper can lead to strong oscillations in the solutions.

The application of ideas and methods of statistical mechanics to problems of biological relevance is one of the most promising frontiers of theoretical and computational mathematical physics.^1,2 Among others, the computer simulation of the immune system dynamics stands out as one of the prominent candidates for this type of investigations.

In the recent years immunological research has been drawing increasing benefits from the resort to advanced mathematical modeling on modern computers.^3,4

Among others, Cellular Automata (CA), i.e., fully discrete dynamical systems evolving according to boolean laws, appear to be extremely well suited to computer simulation of biological systems.⁵

A prominent example of immunological CA is represented by the Celada–Seiden automaton, that has proven capable of providing several new insights into the dynamics of the immune system response.

To date, the Celada–Seiden automaton was not in a position to exploit the impressive advances of computer technology, and notably parallel processing, simply because no parallel version of this automaton had been developed yet.

In this paper we fill this gap and describe a parallel version of the Celada–Seiden cellular automaton aimed at simulating the dynamic response of the immune system.

Details on the parallel implementation as well as performance data on the IBM SP2 parallel platform are presented and commented on.

The implementation of a Monte Carlo code for simulations of liquid crystal lattice models on the Quadrics massively parallel SIMD supercomputer is described. The use of a Quadrics with 512 processors is proving essential in studying the nematic–isotropic phase transition to an unprecedented level of accuracy using more than 10⁶ particles. Here some tests on the Lebwohl–Lasher model with and without an applied field are presented.

We analyze the structure of the periodic trajectories of the K-system generator of pseudorandom numbers on a rational sublattice which coincides with the Galois field GF[p]. The period of the trajectories increases as a function of the lattice size p and the dimension of the K-matrixd. We emphasize the connection of this approach with the one which is based on primitive matrices over Galois fields.

The exact series method is a useful approach for studying critical behavior in the presence of logarithmic corrections to power-law divergences. We describe a visual implementation and several applications of one algorithm for evaluating critical exponents and critical points from series expansions for quantities that exhibit logarithmic forms.

The efficient usage of parallel computers and workstation clusters for biologically motivated simulations depends first of all on a dynamic redistribution of the workload. For the development of a parallel algorithm for the Penna model of aging we have used a dynamic load balancing library, called PLB. It turns out that PLB manages a nearly balanced load situation during runtime taking only a low communication overhead. We compare different architectures like parallel computers and nondedicated heterogeneous networks, and give some results for large populations.

The asymptotic behavior of the density profile of the fluid-fluid interface is investigated by computer simulation and is found to be better described by the error function than by the hyperbolic tangent in three dimensions. For higher dimensions the hyperbolic tangent is a better approximation.

This article discusses the results of simulations of polymer solutions with the Larson model. The point of interest was the relaxation behavior after a temperature jump. It could be shown that the relaxation time is not independent from the polymer size.

The "patch method" of Stuart Kauffman to find the approximative groundstate of a Kauffman-type model is improved by a final optimization and also modified to the groundstate of a ±J Edwards–Anderson spin glass. The method improves simple algorithms and is easily rewritten to other applications.

Simulations with more than 4 × 10¹⁰ sites confirm that the density of active sites in Game of Life cellular automata approaches a positive limit, of about 2.87 per cent.

We perform Monte Carlo simulation using Penna's bit string model, and compare the process of asexual reproduction by cloning with that by genetic crossover. We find them to be comparable as regards survival of a species, and also if a natural disaster is simulated.

We give a full description of a recently developed efficient Monte Carlo Approach to low-lying excitations of one-dimensional quantum spin systems. The idea is in a word expressed as extracting the lower edge of the excitation spectrum from imaginary-time quantum Monte Carlo data at a sufficiently low temperature. First, the method is applied to the antiferromagnetic Heisenberg chains of S=1/2, 1, 3/2, and 2. In the cases of S=1/2 and S=1, comparing the present results with the previous findings, we discuss the reliability of the method. The spectra for S=3/2 and S=2 turn out to be massless and massive, respectively. In order to demonstrate that our method is very good at treating long chains, we calculate the S=2 chain with length up to 512 spins and give a precise estimate of the Haldane gap. Second, we show its fruitful use in studying quantum critical phenomena of bond-alternating spin chains. Using the conformal invariance of the system as well, we calculate the central charge of the critical S=1 chain, which results in the Gaussian universality class. Third, we study an alternating-spin system composed of two kinds of spins S=1 and 1/2, which shows the ferrimagnetic behavior. We find a quadratic dispersion relation in the small-momentum region. The numerical findings are qualitatively explained well in terms of the spin-wave theory. Finally, we argue a possibility of applying the method to the higher excitations, where we again deal with the S=1 Heisenberg antiferromagnet and inquire further into its unique low-energy structure. All the applications demonstrate the wide applicability of the method and its own advantages.